Motion blur for a spotlight projecting an image
That's a real problem. Motion blur only records the difference in position, rotation, size of faces (all visible objects contain faces). From this it calculates speed vectors and blurs regions accordingly. That means objects will be blurry, even their reflections, while lamps (no faces, not directly visible) will show an unblurred spec. 
The same unfortunately goes for animated texture coordinates. There used to be a 'hack' where you would render subframes and combine them, but that multiplies the amount of rendered images by at least 4, usually 8 or more. Let me know if that's an option, then I'll research it again. 
Sorry that's not a solution, but it should contain some answers and it was too big to put it in a comment.